CARTHAGE, Tenn. – Vice President Al Gore yesterday painted over his disagreement with running mate Joe Lieberman on the issue of school vouchers – even as he conceded the issue’s appeal to desperate parents.

Gore, speaking at a school gym in front of his mom, daughter Karenna and about 150 invited guests, said Lieberman’s support for vouchers – which Gore opposes – strengthens the Democratic ticket.

“It’s a strength, not a weakness. An asset not a liability,” insisted Gore, who says selecting Lieberman while knowing those differences shows he’s “not afraid” to run with someone who opposes him.

But the vice president also offered an unsolicited take on why support for vouchers is soaring among some parents, especially at poor schools often found in inner cities:

“If I was the parent of a child who went to an inner city school that was failing … I might be for vouchers, too,” said Gore.

Gore also sought to minimize the separation between himself and Lieberman on Social Security and even on the dicey issue of parental notification for women seeking abortions.

Gore seemed to move closer to Lieberman when he told reporters, “We need to consider them, look at them,” referring to proposals that might require some form of notification.

Earlier yesterday, Lieberman said repeatedly that he plans to express his views on vouchers in private.

“When President Gore decides, Vice President Lieberman will support him entirely,” Lieberman said.

The united front offered by Gore and Lieberman on vouchers marks a strong contrast from the primary season, when Gore hammered fellow Democrat Bill Bradley for supporting vouchers.

Yesterday’s rally, intended to spotlight Gore’s record in Congress on everything from seat belts to infant formula to organ transplants, marked the first full day of campaigning for the duo.

Although both men promised to run positive campaigns, Gore likened his candidacy to the “new guard” and opened his remarks with an attack on the Republican “old guard.”

At one point, Gore waxed nostalgic about a childhood education received inside the walls of Carthage Elementary School.

Gore aides later clarified by saying the veep spent part of second grade at a Carthage public school, although his education was otherwise at an exclusive, all-boys private school in Washington, D.C.

One pitfall for the Gore-Lieberman ticket was illustrated with a stern attack from a local doctor on the health-care industry and insurance companies.

“We’re practicing insurance, and it’s very wrong,” said Dr. R.L. Donaldson, who cared for Gore when the vice president was a child. “Insurance companies and HMO’s are ruining health care.”

Lieberman has collected the most campaign contributions among U.S. senators from the insurance industry, and the Connecticut senator is considered a key ally in Congress.

Doug Hattaway, a Gore spokesman, said Lieberman’s ties to the insurance industry don’t pose a problem, since the election is focused on the broader issue of a patient’s bill of rights.